8x-x/x*8-x=-2/15

Solution for 8x-x/x*8-x=-2/15 equation:

8x-x/x*8-x=-2/15

We move all terms to the left:

8x-x/x*8-x-(-2/15)=0


Domain of the equation: x*8!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-x/x*8-(-2/15)=0

We get rid of parentheses

7x-x/x*8+2/15=0

We calculate fractions


7x+(-15x)/120x+128x/120x=0

We multiply all the terms by the denominator


7x*120x+(-15x)+128x=0

We add all the numbers together, and all the variables

128x+7x*120x+(-15x)=0

Wy multiply elements

840x^2+128x+(-15x)=0

We get rid of parentheses

840x^2+128x-15x=0

We add all the numbers together, and all the variables

840x^2+113x=0

a = 840; b = 113; c = 0;
Δ = b2-4ac
Δ = 1132-4·840·0
Δ = 12769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12769}=113$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-113}{2*840}=\frac{-226}{1680}
=-113/840
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+113}{2*840}=\frac{0}{1680}
=0
$